Question

Debasish gains utility from consumption of bananas, where the utility he gains from consuming b kilograms bananas is -2b2 + 240b + 2.

Suppose the price of bananas is 60. At this price, what is Debasish's quantity demanded for bananas (assuming he is maximising utility).
Please give your answer as a single number. You do not need to write 'kilograms'.

Answer 1

Debasish's quantity demanded for bananas at the price of 60 is 45 kilograms, calculated by setting the marginal utility equal to the price and solving for the quantity.

Step-by-step explanation:

To determine Debasish's quantity demanded for bananas given the utility function -2b2 + 240b + 2 and the price 60, we should find the point where the marginal utility per dollar spent is maximized. To find this, we compute the marginal utility by taking the derivative of the utility function with respect to the quantity of bananas, b, and then set that equal to the price, to solve for b. The calculated quantity demanded will be the number of kilograms of bananas Debasish will want to consume to maximize his utility at the given price.

First, we take the derivative of Debasish's utility function, U(b) = -2b2 + 240b + 2, to find the marginal utility, which is MU(b) = -4b + 240. Next, we set MU(b) equal to the price to find the utility-maximizing quantity:

-4b + 240 = 60

Then solve for b:

-4b = 60 - 240

-4b = -180

b = 45

Thus, at the price of 60, Debasish's quantity demanded for bananas is 45 kilograms.